#include<bits/stdc++.h>
#include "game.h"
using namespace std;
#define tm (p.tl+p.tr >> 1)
#define mp make_pair
#define pb push_back
#define st first
#define nd second
typedef long long ll;
const int mod = 1e9 + 7;
const int N = 2e5 + 5;
inline ll gcd(ll u, ll v) {
ll r;
while (v != 0) { r = u % v; u = v; v = r; }
return u;
}
struct node{
ll x;
int tl, tr;
struct node *l, *r, *to_y;
node() { x = 0; l = r = to_y = NULL; }
} root;
node* nw(int l, int r){
node* p = (node*) malloc(sizeof(node));
p -> tl = l; p -> tr = r;
return p;
}
ll qry_y(node &p, int ly, int ry) {
if(ly > p.tr || ry < p.tl) return 0;
if (ly <= p.tl && p.tr <= ry) return p.x;
return gcd(p.l ? qry_y(*p.l,ly,ry) : 0 , p.r ? qry_y(*p.r,ly,ry) : 0);
}
ll qry_x(node &p, int lx, int rx, int ly, int ry) {
if(lx > p.tr || rx < p.tl) return 0;
if (lx <= p.tl && p.tr <= rx) return p.to_y ? qry_y(*p.to_y,ly,ry) : 0;
return gcd(p.l ? qry_x(*p.l,lx,rx,ly,ry) : 0 , p.r ? qry_x(*p.r,lx,rx,ly,ry) : 0);
}
void up_y(node &p, int py, ll val){
if(p.tl == p.tr){ p.x = val; return; }
if(py > tm) { if(p.r == NULL) p.r = nw(tm+1,p.tr); up_y(*p.r,py,val); }
else { if(p.l == NULL) p.l = nw(p.tl,tm); up_y(*p.l,py,val); }
p.x = gcd(p.l ? p.l->x : 0 , p.r ? p.r->x : 0);
}
void up_x(node &p, int px, int py, ll val){
if(p.tl < p.tr){
if(px > tm) { if(p.r == NULL) p.r = nw(tm+1,p.tr); up_x(*p.r,px,py,val); }
else { if(p.l == NULL) p.l = nw(p.tl,tm); up_x(*p.l,px,py,val); }
val = gcd(p.l ? qry_y(*(p.l->to_y),py,py) : 0 , p.r ? qry_y(*(p.r->to_y),py,py) : 0);
}
if(p.to_y == NULL) p.to_y = nw(0,mod); up_y(*p.to_y,py,val);
}
void update(int x, int y, ll val){
up_x(root,x,y,val);
}
ll calculate(int lx, int ly, int rx, int ry){
return qry_x(root,lx,rx,ly,ry);
}
void init(int a, int b) { root.tl = 0; root.tr = mod; }
